# Question Video: Calculating a Correlation Coefficient from Calculated Sum of Squares

A data set has summary statistics π_(π₯π₯) = 36.875, π_(π¦π¦) = 73.875, and π_(π₯π¦) = 32.375. Calculate the product-moment correlation coefficient for this data set, giving your answer correct to three decimal places.

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### Video Transcript

A data set has summary statistics π π₯π₯ is equal to 36.875, π π¦π¦ is 73.875, and π π₯π¦ is 32.375. Calculate the product-moment correlation coefficient for this data set, giving your answer correct to three decimal places.

We are given the summary statistics for a data set, where π π₯π₯ is 36.875; thatβs the variation in π₯. π π¦π¦ is 73.875; thatβs the variation in π¦. And π π₯π¦ is 32.375; thatβs the covariance of π₯ and π¦. And using these summary statistics, we want to calculate the product-moment correlation coefficient. To do this, we can use the abbreviated form of the correlation coefficient formula. That is, the correlation coefficient π π₯π¦ is π π₯π¦ divided by the square root of π π₯π₯ times π π¦π¦.

Since weβre given the summary statistics, we simply need to substitute these into the formula. So that π π₯π¦ is 32.375, thatβs π π₯π¦, divided by the square root of the product of 36.875, which is π π₯π₯, and 73.875, which is π π¦π¦. That is 32.375 over the square root of 2724.140625, which is 32.375 divided by 52.19330 to five decimal places. And thatβs approximately 0.62029. And so to three decimal places, the product-moment correlation coefficient for this data set is π π₯π¦ is equal to 0.620.